Solve [(-3)^{9}*2^{2^6}]:(-6^8)+(-2^6)^3

$$[ ( - 3 ) ^ { 9 } \cdot 2 ^ { 2 ^ { 6 } } ] : ( - 6 ^ { 8 } ) + ( - 2 ^ { 6 } ) ^ { 3 }$$

Evaluate

$$216172782113521664$$

Solution Steps

Calculate -3 to the power of 9 and get -19683.

$$\frac{-19683\times 2^{2^{6}}}{-6^{8}}+\left(-2^{6}\right)^{3}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{-19683\times 2^{64}}{-6^{8}}+\left(-2^{6}\right)^{3}$$

Calculate 2 to the power of 64 and get 18446744073709551616.

$$\frac{-19683\times 18446744073709551616}{-6^{8}}+\left(-2^{6}\right)^{3}$$

Multiply -19683 and 18446744073709551616 to get -363087263602825104457728.

$$\frac{-363087263602825104457728}{-6^{8}}+\left(-2^{6}\right)^{3}$$

Calculate 6 to the power of 8 and get 1679616.

$$\frac{-363087263602825104457728}{-1679616}+\left(-2^{6}\right)^{3}$$

Divide -363087263602825104457728 by -1679616 to get 216172782113783808.

$$216172782113783808+\left(-2^{6}\right)^{3}$$

Calculate 2 to the power of 6 and get 64.

$$216172782113783808+\left(-64\right)^{3}$$

Calculate -64 to the power of 3 and get -262144.

$$216172782113783808-262144$$

Subtract 262144 from 216172782113783808 to get 216172782113521664.

$$216172782113521664$$

Factor

$$2^{18}\times 824633720831$$